COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Field Theory * MT   412 8 3 3 5

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Prof.Dr. Gonca AYIK
Instructors
Prof.Dr.GONCA AYIK1. Öğretim Grup:A
Prof.Dr.GONCA AYIK2. Öğretim Grup:A
 
Assistants
Goals
Genaral aim of this course is to teach the Galois theory and some of its results.
Content
Review of theory of rings, field extension, simple and transcendental extensions, degree of an extension, ruler and compass constructions, Galois group of an extension, splitting fields, normal and separable extensions, solution of equations by radicals.

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
X
10
Uses effective scientific methods and appropriate technologies to solve problems
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Review of basic concepts from Ring theory Review of related concepts from lecture notes and sources
2 Decomposition in polynomial rings Review of related concepts from lecture notes and sources
3 Field extensions Review of related concepts from lecture notes and sources
4 Classification of simple extensions Review of related concepts from lecture notes and sources
5 Degree of an extension Review of related concepts from lecture notes and sources
6 Ruler and compass construction Review of related concepts from lecture notes and sources
7 Principles of the Galois Theory Review of related concepts from lecture notes and sources
8 Mid-term exam Review of topics discussed in the lecture notes and sources
9 Splitting fields Review of related concepts from lecture notes and sources
10 Finite filelds Review of related concepts from lecture notes and sources
11 Monomorphisms between fields and Galois Groups Review of related concepts from lecture notes and sources
12 Normal and separable extensions Review of related concepts from lecture notes and sources
13 Normal closure Review of related concepts from lecture notes and sources
14 Galois relation of an extension. Review of related concepts from lecture notes and sources
15 Galois relation of an extension Review of related concepts from lecture notes and sources
16-17 Final exam Review of topics discussed in the lecture notes and sources

Recommended or Required Reading
TextbookI. Stewart, Galois Theory, Chapman and Hall, London 1973
Additional Resources
John M. Howie, Fields and Galois theory, Springer- verlag London, 2006